Date of Award


Publication Type

Master Thesis

Degree Name





Drake, Gordon W. F.


Quantum physics, Atoms & subatomic particles, Theoretical physics




The critical nuclear charge Z c for a three-body quantum mechanical system consisting of positive and negative charges is the minimum charge for the system to remain in a bound state. This work presents a study of the critical nuclear charge for heliumlike systems with infinite nuclear mass, and also a range of the reduced mass up to 0.5. The results help us to resolve a discrepancy in the literature for the infinite mass case, and they are the first to study the dependence on reduced mass. It is found that Z c has a maximum at [Special characters omitted.] mM = 3525, which is intermediate between the atomic structure of helium, and the molecular structure of [Special characters omitted.] H+2 . Z c for the infinite mass case is found to be 0.911028267. This value is compatible with the result of Baker, et al, who found the upper bound for Z c to be 0.91103. However, it does not agree with other results in the literature. The understanding of the critical charge will bring us a deeper appreciation of the stability of a three-body system as a function of the reduced mass, correlation effects of coulombic potential and more importantly, the physics of a three-body quantum mechanical system.